Definition of check back
Generally, when we talk about check-back, we are talking about a two-player situation after the flop. To check back, you have to be in position, i.e. you have to talk last on each betting round. Generally, a player will check back to take the pulse of his opponent (a check back is a check after a check, that of our opponent). He takes advantage of his position to get as much information about his hand as possible. It is quite rare that a player will check back a flop with a big hand (although a player may have his reasons for doing so).
Reasons to check back
We can check back for many reasons. You can check back to keep the pot small or because your hand is too strong. Or because you are not sure of your opponent's range. For example, you open in UTG position with a pair of jacks and a tight player over-raises you (3bet) from the small blind. Here, there's no need to do anything but call. The flop comes 2-2-8 and your opponent checks out of position. You suspect he has AA or KK who is preparing to check-raise all in to make you pay your JJ and QQ. He could also have an AK that missed the flop. You're not sure, so after he checks, you decide to check back to get more information about his hand on the turn.